Jacob Perlman, a calculus lecturer for the University of Chicago, joins Tom and Tony to discuss a well-known metric referred to as “Value-at-Risk.”

In finance, the term Value-at-Risk (VaR) is a commonly used measure that helps to quantify a portfolio’s risk in a specified time frame by using a certain confidence/probability level (95% and 99% are the more commonly used levels). In every calculation we must choose a certain confidence level and time frame in which to calculate our VaR.

For example, VaR can tell us, “5% of the time I can expect to lose $10,000 or more over any given 10 day period (time frame).” In this example, the 5% confidence interval and 10 day time frame are variables chosen by us, whereas $10,000 is the result of the VaR calculation.

When applying VaR to a given portfolio, Jacob warns against misusing the metric by assuming the value computed from VaR is the worst-case scenario. In reality, the VaR number generated by the formula is merely a starting point, but of course the loss can be much higher than what VaR suggests.

Transcription:

Tony: Thomas we're back my friend. The skinny on option math.

Tom: Hello Jacob. We'll start over again.

Tony: The technology of the internet. We'll start over again.

Jacob, how you doing?

Jacob: I'm pretty good how are you?

Tony: I'm doing okay thank you. Who’s your huckleberry?

Tom: What?

Jacob: It's from a movie. It's from Deadwood.

Tony: Mm hm. (affirmative)

Tom: A little older.

Jacob: Tombstone.

Tony: Tombstone. Correct.

Tom: You guys are good.

Tony: Thank you.

Tom: You guys are good. What do we got going on today?

Tony: I want to talk about value at risk because it's a number that I think people see thrown around and I think that a lot of people have only a vague idea of what it means, and that it's probably worth understanding what this means when people start talking about it.

Tom: value at risk.

Jacob: value at risk.

Tom: Okay.

Jacob: This is … It's more often used in lar- … It's less often used in individuals, in an individual portfolio than it is in larger scale things, but it still is a relatively commonly discussed concept. It's one that's pretty easy to misunderstand because it sounds like it means something that it doesn’t.

Tom: Explain please.

Jacob: The phrase value at risk maybe sounds like, “How much money you're risking.” Like how much you could lose. That's just not what value at risk means. Value at risk is a related idea, there's a reason it's called what it's called, but the actual thing that value at risk is, is it needs you to specify a probability and a time frame. Then value at risk is the amount that have that probability-, you have that probability of losing that amount or more in that time frame. One of the major problems I think people run into when they start trying to think about value at risk is that it's an “or more”. It's not … The “or more” is inherently part of the poorly defined regime of … Because it's out in the tails, it's these low probability events, because usually the probabilities that you use for value at risk are things like, “One or five percent.” Once you get out there into these tail events, that’s really where our models have their flaws. We know that our models, like our Black Scholes models and things, are very good in the bulk, for the typical type behaviors, but that there's something wrong out in the tails, there's some sort of skew or fat tail in this that's not really in there in the normal distribution. Value at risk makes you extra vulnerable to that if you use it incorrectly.

Tom: I thought an “or more” was like a calf.

Tony: A calf?

Tom: I thought an “or more” was like a cow, something like that but I guess not.

Tony: Or more

Jacob: Or more.

Tony: In a world of trading you know what we call it? “Or Better.”

Jacob: Well, in this case it's “or worse”, it's lost.

Tom: There's no order that you'll ever give to a broker that says, “Or worse.” What you essentially want to do is, “Or Better.” You're sending a subliminal message, “Or better.” Okay? “Or better.”

Jacob: You will lose a million dollars, or better?

Tom: value at risk is a widely used measure for the risk of a portfolio, for a given time frame and probability the value at risk is the amount of loss that has the given probability to be exceed in the timeframe. The value if … What’s V in this case?

Jacob: The value of the portfolio type T.

Tom: Okay, so the value of the portfolio. If the value of the portfolio is the value of the portfolio times time, then you have this formula, which I don’t know what it means.

Jacob: Right, so this just says that the value at risk is the smallest amount of loss where the probability of losing that amount or is [crosstalk 03:44]-

Tony: Explain to me in … Give it to us in lay terms. What does it mean? If I have a portfolio that is worth, let’s say a hundred dollars. If I have a portfolio that's worth a hundred dollars, how am I supposed to assess … What would my value at risk be?

Jacob: You would need to know more of your model and the structure of your portfolio not just its current value. Then if someone might say, “Your value at risk for your one week, five percent value at risk is maybe forty dollars.”

Tom: Yeah, but what's that based on?

Jacob: That's based on your models-

Tom: Let’s say my model is, I have a very-

Jacob: Is Black Scholes, or-

Tom: Right, whatever my model is. My model is let’s just say a bunch of independent positions where I believe I'm Delta Neutral but I have some short premium. How would I figure out my value at risk?

Jacob: Your value at risk … In practice the two ways that are usually used to compute it are either Monte Carlo simulations, where they’ll just run a lot of experiments and try to see, or historical simulations. Where they’ll use historical data about how much movement they had in these various underlyings and positions, and try to come up with an aggregate simulation. In principle if you were doing something like that where-

Tom: So, how-

Jacob: … you have a bunch of independent Black Scholes kind of thing-

Tom: How does-

Jacob: … you could do an explicit computation with some probability distributions.

Tom: How’s that help an individual investor? Is it something that's … I mean … You give me a number, how am I supposed to assess that and how does that help an individual investor?

Jacob: There's the immediate way people think about using it, and how it actually has a use. The immediate way people think about using it is they think about it as, “Oh, well I'm not going to lost more than … I'm unlikely to lose more than that.” That's what it promises by its name, but that's not really what it's good for. If it has any use, what it's good for is it tells you where the cut-off is between where, what you would think of as typical movements where your probabilities are going to be reliable, where all these predictions are going to come out relatively true, and then these tail events where we expect our probability models to be worse. Anytime you have a loss bigger than your value at risk, you should start becoming very suspicious of all of your probabilities. That's where all of your probabilities are going to start being weird, because we're in some sort of large movement where our models are worse.

Tom: The primary use for the value at risk is a cut-off between what are seen as typical movements, and the so-called tail movements, so it's really a way to … The way we would assess that, because we get this question all the time, is we wouldn't be able to explain value at risk, we would essentially say, “We have to look at it as: what is the statistical chance of getting out to those tails?” We would argue that depending on … We would use the same risk that most brokerage firms’ use, rather than … What you're saying here is pretty much this is some portfolio, as a way of looking at a portfolio as opposed to looking at individual tail risks?

Jacob: You could look at … You could do it on an individual trade rate. You imagine your portfolio as just a single position and do it there. There's a disadvantage to doing it that way, which we'll get to later where “not at risk” is not sub-additive. Just because you know the value at risk for two positions doesn’t mean that you know the value at risk for them combined, or even that you have a bound on it. They toge- … The two positions combined can have a much worse value at risk than the two separately might indicate.

Tom: Got it.

Jacob: That's the reason that it's generally done for portfolios as a whole rather than as individual positions, because doing individual positions you can't then add up they’ll cross them.

Tom: Got it. What good is knowing the value at risk? We've just been discussing that. It is widely recognized that existing models for the market are good in the bulk are flawed with how they treat the tails. Do you think that people, traditional portfolio models, how relevant is tail risk? I've always wondered this before, we talk about tail risk because we trade a lot of naked derivative products with a lot of leverage, but if you're non-levered how valuable is tail risk?

Jacob: I think you still have to be very concerned about tail risk just because tail risks are where the crashes are. They're where the sun surges and where the crashes are, and where the huge shifts come from. If you're completely unprepared for them, they don’t happen very often but they do happen, and they will happen to you eventually. The value at risks are usually done with one or five percent. One or five percent isn’t that unlikely. That's a couple times a month, or a couple times a year.

Tom: How much different is that than just normal probability of X trading at X?

Jacob: The real key to the value at risk number, if you want to use it for something, is that up until you got to value at risk, if your value at risk is reasonably computed, then your probability at X trading at Y is a good probability. That's a trustworthy number. Out past value at risk you want to start being real suspicious about what those numbers say, because they're not going to be as reliable.

Tom: Outside of … When it gets to the dark spot-

Jacob: I think it's called “value at risk break”.

Tom: Value at risk break, okay I didn't know what it was called, okay got it. The value at risk number can be computed for a position that is not too small can give you a good definition of how much movement your holdings might take without leaving the bulk, and the models can generally be trusted when realized losses don’t exceed the value at risk.

Jacob: Right. The real key is-

Tom: That's pretty-

Jacob: … once you-

Tom: … common sense.

Jacob: … had a value at risk break you want to start … You don’t want to trust your probability of X trading at Y numbers as much, because those are going to become much less reliable numbers.

Tom: Because at that point you're probably talking about all the volatility models have changed dramatically.

Jacob: You're out in the tail event where we don’t really think the normal distribution is correct anymore, and we don’t really think that the [inaudible 09:16] model is really right in these situations. Because we have some sort of-

Tom: Is that mostly downside risk you're talking at that point?

Jacob: Yeah, so value risk is-

Tom: Is that bankruptcy risk, or whatever-

Jacob: Value at risk is only measuring-, is only to the downside, just by definition, in practice that's where more of the issues are.

Tom: Because people aren’t sure?

Jacob: Right.

Tom: I'm starting to put this whole thing together now, because-

Tony: I'm glad you're getting it.

Tom: How far … We've come so far with our modeling technol- … Do you know what I mean?

Jacob: Yeah.

Tom: What bothers me is I kind of feel value at risk is an old method.

Jacob: It is, it's from right after the crash of ’87 when they need to have something like, “Oh, what happened, how do we avoid this happening? Where did our-“ The realization was that the models did not correctly predict-, during these large motions, the models broke down. The value at risk is a good way to look at, “What is the point where we have to stop trusting our models?”

Tom: Right, is the take-away here going to be that our technology is better, our models are better and we've made the adjustments in pricing, like whatever it is, skew, volatility, there's different asset classes right now, is that the take-away?

Jacob: Our models are better, but because value at risk is specifically about these rare events, our models will never be-, can never be that good because we won't have enough instances. There's not going to be enough data points to go there, to really get a good model. We're not going to be able to build a good model for these tail events because they don’t happen often enough.

Tom: On the other hand, during a value at risk break, investors should be aware the probability models can be-, are used to compute pretty much every financial metric and they become unreliable. Yeah, that's the whole thing, that's the risk that we never talk about, that's that … Some people use the term Black Swan, cra-, whatever you want to do but that's right, that's when the financial markets become unstable.

Jacob: Right, the thing is when your probabilities are the difference between thirty percent of being here, and twenty percent of being there, it's probably good. Those are probably good numbers where we have lots of data and our models are good. When you're probabilities are telling you the difference between something being .05% likely, and .025% likely, don’t trust it, that-, things are probably not actually twice as likely as the other.

Tony: We had this discussion yesterday morning when somebody wrote an email about selling cheap SPX puts, and our response to the cheap SPX puts question was … He goes, “Well theoretically they're way too rich.” We're like, “Well, forgot about what's theoretical at that point. When you're talking about something that is a three standard deviation move, the reason for doing that is completely different.” That's about units, and it's about controlling capital costs, it has nothing to do with value at that point.

Jacob: Right, because you're out past the point where the “theoretical richness” is … We've gotten to the point where that's not a meaningful number.

Tom: That's right because nobody’s going to sell stuff for …

Tony: At thirty seven cents, or forty two cents, it doesn’t matter anymore.

Tom: The difference is, if somebody said to you tomorrow, “Will you sell the next lottery ticket.” You know there's only a one in 175 million chance of that lottery ticket winning, so you'd like to take the dollar, but on the small chance that you lose a hundred million-

Jacob: You can't cover it.

Tom: … you can't cover it, right.

Tony: It's an airport trade.

Tom: Yeah, that's the situation here. I think it's an important conversation to have, but I want people to recognize that no matter what we talk about on this show, if the kind of the “shit hits the fan” type thing, it's … There's a lot more problems. You have problems with the technology, you have problems with the quote delivery, and you can't get orders through. The key to all of this, there's only one take-away that you start here that's been so valuable you stay small.

Jacob: Yeah.

Tom: … that's you're take-away.

Jacob: You want to keep in the bulk, you want to stay to where the models are good, and the models are good in the normal behaviors.

Tom: You can basically look at a worst, worst, worst case, and as long as you're small enough you're in there. Since value at risk requires computing probability of movements in the market, it depends strongly what methods are being used to compute those probabilities. Some institutions base their VAR computations on historical models, while other use Monte Carlo methods, but you shouldn't put too much worth in a number without knowing where it came from.

Jacob: Right, large investment firms publish their value at risk numbers; they're on the first spreadsheet that they planned out. You really need to look at how they came up with those numbers-

Tony: I've always-

Jacob: … just them telling the numbers-

Tony: … despised those numbers.

Jacob: … is not a meaningful thing.

Tony: I despise value at risk because, to me … Here, and this is kind of why I'm so happy you covered this today. To me, it's garbage, because if you don’t reduce basis … Seriously, if you don’t reduce basis, you can give me all the value at risk numbers you want, it's still a fifty-fifty shot without them understanding what the downside risk is.

Jacob: Right.

Tony: But if you reduce basis, then you have a whole different argument. Even if value at risk is computed perfectly the number could be misleading. Firstly, it is the loss that will be exceeded a given percentage of the time. In those time maybe exceeded quite severely due to the fat tails of financial distributions. This is like, “Yeah, you can keep selling lottery tickets, and you may be able to sell 250 million, before you lose one lottery, but nobody cares about that.”

Jacob: The important thing is when actual lotteries sell lottery tickets, they know they’re selling one winner and all the others are losers. They're not actually taking risk. If you went out there and you sold things that you had to pay out 800 thousand dollars one in a million times, that would be bad odds, or you'd be making money every time probabilistically but you'll lose sometimes. When you get a bad loss-

Tom: When you have to split the pot.

Jacob: … when you have an unlikely thing and two people won. When two people win in a day-

Tom: They split the pot.

Jacob: … you're screwed.

Tom: In that example, but the way the lottery does it, you just split the pot.

Jacob: Yeah, they split the pot; they know exactly how much they have to pay out at the end before they start. That makes it safe for them to sell lottery tickets, but these “way out of money” puts that you want to sell-

Tony: It defines the risks-

Jacob: … those are lottery tickets.

Tom: The best case scenario for them is they sell a half a billion dollars, instead of the 175 million-

Tony: And half a billion win.

Tom: Yeah, this is-

Tony: Everybody wins.

Tom: Let’s go to the next one, anyway … Secondly, the percentages can be misleading, remember sometimes that happens five percent of the time will happen more than once a month.

Jacob: Right, a lot of people think the value at risk is these-, a very unlikely thing, but it's usually found in one in five percent. One in five percent are not that unlikely. You interact with them … You have a one in five percent odds everyday of your life.

Tom: It's the way-, the financial community is build around the five percent number. Five percent is the two standard deviation move, five percent is everything in this business, everything is build around, risk wise, and everything is built around five percent. It's funny that five percent is the same number you come up with there.

Jacob: Right, it's the standard one that gets use. Remember five percent is not that unlikely. If you flip five coin you'll likely … If you flip five coins, you're less than five percent to get five heads, but honestly you'll get five heads one in thirty-two times. That doesn’t take you that long to try.

Tom: Agreed. Another issue is that value at risk is not sub-additive that is, “That value at risk for a portfolio can be larger than sum-“, which is what you're saying, “… of the components so trying to estimate value at risk by looking at some of the component of a portfolio can result in thinking that there's less risk than there really is.” I would say then that the answer … That the solution to this is getting back to what we do here. Again, nobody else does this stuff, which is the non-, the really understanding non-correlated underlyings. Because I can see, listen, if you have five different positions on, and we go to hell, it doesn’t matter if they're five different index positions-

Jacob: Right.

Tom: … but if you have completely … If one of those positions is corn, you know or wheat or one of those positions is bonds. You have a non-correlated … It's not going to be every single one is going to be-

Jacob: Right, they're not all going to tank all at once.

Tom: That's right.

Jacob: The real problem with trying to add up you're value at risk of things is that there's a lot of correlations that make … When one of them took a large downside; they all took a large downside.

Tom: That’s great, this was a very helpful because what it does, I think it a little bit de-mystifies that whole myth of … I hate that myth of value at risk, “Our value at risk numbers are …” whatever, you know. That drives me crazy.

Jacob: Right, people spend their time … There are lot who spend their time trying to control value at risk and this is psychotic.

Tom: Yeah, how do you control something that you … How do you control something that you have no idea when it will happen or why it will happen?

Jacob: Right, and then anytime it does occur, you’re well beyond any of your models giving you good predictions, you've entered chaos land.

Tom: Again, getting back to the simplest bits of advice for individual investors, which is so important, independent occurrences-

Tony: Number of occurrences.

Tom: … independent non-correlated occurrences and staying small. This gets back to, if every individual investors understood this or was able to conceptualize this, their ability to articulate portfolio management blows away the whole industry. That's what we're trying to get to, lots of independent, small, non-correlated events/occurrences, and other than that it really doesn’t matter.

Jacob: Yeah. Volatility is mean reverting and everything else is random.

Tom: We just did a thing on volatility on how fast it goes down relative to going up. We looked at four different underlyings during our market measure today and we saw that anywhere from, it could be as much as 4x to .5x depending on the underlying. Whether it was a commodity or just a stock index, on how fast volatility goes down relative to volatility going up. It's really fascinating because when you see that and you combine it with this, that's special.

Tony: Pretty powerful.

Tom: It's really powerful.

Tony: Let’s take a quick break, we'll come back, we've got our boot-strapper next, this is tastylive Live.